A remark on the convergence of Betti numbers in the thermodynamic regime

Springer Science and Business Media LLC - Tập 9 - Trang 1-7 - 2017
Khanh Duy Trinh1
1Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

Tóm tắt

The convergence of the expectations of Betti numbers of Čech complexes built on binomial point processes in the thermodynamic regime is established.

Tài liệu tham khảo

Bobrowski, O, Kahle, M: Topology of random geometric complexes: a survey. Topology in Statistical Inference, the Proceedings of Symposia in Applied Mathematics. to appear.

Meester, R, Roy, R: Continuum Percolation. In: Cambridge Tracts in Mathematics, p. 238. Cambridge University Press, Cambridge (1996).

Munkres, JR: Elements of Algebraic Topology. Addison-Wesley Publishing Company, Menlo Park (1984).

Nakamura, T, Hiraoka, Y, Hirata, A, Escolar, EG, Nishiura, Y: Persistent homology and many-body atomic structure for medium-range order in the glass. Nanotechnology. 26(30), 304001 (2015).

Penrose, M: Random Geometric Graphs. In: Oxford Studies in Probability, p. 330. Oxford University Press, Oxford (2003).

Penrose, MD: Laws of large numbers in stochastic geometry with statistical applications. Bernoulli. 13(4), 1124–1150 (2007).

Penrose, MD, Yukich, JE: Weak laws of large numbers in geometric probability. Ann. Appl. Probab. 13(1), 277–303 (2003).

Yogeshwaran, D, Adler, RJ: On the topology of random complexes built over stationary point processes. Ann. Appl. Probab. 25(6), 3338–3380 (2015).

Yogeshwaran, D, Subag, E, Adler, RJ: Random geometric complexes in the thermodynamic regime. Probab. Theory Relat. Fields. 167(1-2), 107–142 (2017).

Thông tin
Thông tin xuất bản

Springer Science and Business Media LLC

Tập 9

1-7

Thông tin tác giả